NEW YORK — The Washington Capitals didn’t just lose a second-round playoff series in seven tight, tough games with the top-seeded New York Rangers here in thunderous Madison Square Garden on Saturday night. This was a defeat with a victory of a different but enormously important kind, hidden inside it.

The Caps reasserted, even in their 2-1 loss at the hands of superb goalie Henrik Lundqvist, that they have found a new playing style — a new team identity really — under rookie Coach Dale Hunter that can keep their Window of Opportunity as a serious Stanley Cup contender open for years.

An era has not ended. A five-year period of Young Guns and end-to-end, highlight-film scoring plays has not crashed bitterly. Instead, it has been transformed internally — with many of the same players on the ice, but with all the Caps approaching the game completely differently.

The sometimes selfish, often unfocused and occasionally downright demoralized Caps of the past four postseasons have, apparently disappeared. Instead, the Capitals have coped with the gradual aging, injury and erosion of some of their brightest stars and have adjusted on the fly — made a midcourse correction, one of the most difficult tasks in sport.

“It’s the right way to play to win it,” Hunter said of the Stanley Cup quest. “You see the teams that are left. It’s tough hockey, tooth and nail.

“It’s tough [to lose] and it should be tough. We were just a goal short.”

In the past, what Washington often lacked was much more than a goal. It was a combination of qualities that command respect in the NHL and which Hunter, of course, calls character. He might as well say “pain in pursuit of progress,” because everything he demands hurts in one way or another.

Whether a Capitals player must throw his body in front of slap shots, bang on the boards, focus on defense first or sacrifice minutes so the right players, by skill-set, not star reputation, can be on the ice at the proper times — there is always an element of sacrifice. That, always and everywhere, leads to the key word in team sports, which would be. . . come on, you know. . . “TEAM.”

The thing the recent Caps have never really been.

“Everyone played their hearts out,” defenseman John Carlson said. “We had a bunch of warriors in here who were willing to do whatever it takes. We just didn’t get the bounced this time. Lundqvist just came up huge for them. It [stinks].”

Athletic grief — and this game had it — at least brings dignity and, eventually, promise for the future. Perhaps you have to have stood in too many Capitals’ season-ending locker rooms when the word “chokers” hung in the air — like a cartoon bubble above the heads of the Caps themselves — to know what progress this genuine, hard-earned sadness really is.

This narrow loss will hurt for days and weeks, especially because the Caps allowed a Brad Richards goal just 92 seconds into the battle; that lone score set a tone for the entire evening. The team that scored first won every game in this series. Washington, which fell behind 2-0 at 10 minutes 5 seconds into the third period, but made it a game again when Roman Hamrlik scored just 38 seconds later, seemed under that spell all night. Hard verdict: behind for 58:08.

Tough as this defeat will be to digest — the Caps have now played 13 games decided by a single goal in 14 postseason contests — something important will endure after this defeat recedes into the summer. Viewed in the context of the next several seasons, the Capitals found an identity — something they’ve been looking for five years and just discovered in the past five weeks.

“This is the best team I’ve been on,” defenseman Karl Alzner said. “We could yell at each other. Guys grew tremendously. We became better players and people. We’re still working out the kinks. We’ll get better.”

Less than two months ago, you heard calls to “break up” the current Caps, built on the Alex Ovechkin, Nick Backstrom, Alexander Semin, Mike Green core, because their “window” was obviously closing. Wasn’t Backstrom back in Sweden recovering from a concussion? Hadn’t Green been injured — again? Weren’t Semin’s goal totals down?

The drumbeat built: Fire General Manager George McPhee, maybe get rid of this new coach, too. Just say, “Damn it,” a few dozen times, then start setting the dynamite charges. This seductive impulse toward destruction seldom produces the desired results in pro sports. Instead, it often means years in the wilderness of rebuilding.

Now, all those fears, and all those potential decisions, can be shelved. Ultimately. this season served its purpose.

Why? Because the Capitals’ Stanley Cup hopes are no longer predicated on young legs leading a high-scoring, wide-open team. Now, they don’t have to fade if Ovechkin’s yearly point totals continue to shrink or any one offensive star becomes a disappointment. Now, less conspicuously-skilled players can be central players. The Caps can reload and reform themselves, not blow things up.

Assuming Hunter wants to return as coach, and McPhee will beg and bribe to get him back, the Caps suddenly find themselves at the beginning of a process, not at the end of an era.

In the history of the NHL playoffs, the record for one-goal games is 16, set in ’06 by Carolina in four series. In just two series, the Caps had 13 one-goal games. That close-to-the-vest style defines the current Caps. But it also shows that, with reasonable offseason improvement — and perhaps home-ice advantage in future postseason series — deeper playoff runs are on the agenda.

Perhaps the greatest nag is that the Caps, in Alzner’s words, “had perfect health right now. You don’t know how often that will happen.”

Unlike so many previous Cap playoff teams, this one didn’t crack under pressure but rather responded with retaliation, even when the Rangers beat them in triple overtime, even when New York scored with 7.6 seconds remaining in regulation then won in overtime.

And they found their goalie in rookie Braden Holtby, who played a quality game just two days after his fiancee gave birth to their first child. Call me crazy, but at 22, coping with childbirth and a Game 7 in Madison Square Garden sounds like a fellow with fairly good focus.

“He’s played well under extreme pressure against [Tim] Thomas [in the seven-game win over Boston] and Lundqvist, who could be MVP of the league. He played ’em even,” said Hunter in what amounts to a soliloquy for him. “I’m proud of him.”

Perhaps only ardent Capitals fans, who endured the previous four postseasons, the firing of Bruce Boudreau and an infuriating regular season, could fully appreciate how far this franchise has been revitalized in a matter of weeks.

Just two months ago, the Capitals were a team without style or substance. Or, rather, because they had no defined style of play — no deep commitment to a common and often painful plan — all their disconnected talents amounted to little NHL substance.

Now, even in a season-ending defeat, they have what they needed most — the clear outline of a bright, though radically different Capitals future.

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